A322052
Number of decimal strings of length n that contain a specific string xy where x and y are distinct digits.
Original entry on oeis.org
0, 1, 20, 299, 3970, 49401, 590040, 6850999, 77919950, 872348501, 9645565060, 105583302099, 1146187455930, 12356291257201, 132416725116080, 1411810959903599, 14985692873919910, 158445117779295501, 1669465484919035100, 17536209731411055499, 183692631829191519890, 1919390108560504143401
Offset: 1
Suppose the desired string is 03. At length 2 that is the only possibility. At length 3 there are 20 strings that contain it: 03d and d03, where d is any digit.
-
f:= gfun:-rectoproc({10*a(n) - 101*a(n + 1) + 20*a(n + 2) - a(n + 3), a(0) = 0, a(1) = 0, a(2) = 1},a(n),remember):
map(f, [$1..40]); # Robert Israel, Mar 27 2020
A322054
Number of decimal strings of length n that do not contain a specific string xx (where x is a single digit).
Original entry on oeis.org
10, 99, 981, 9720, 96309, 954261, 9455130, 93684519, 928256841, 9197472240, 91131561729, 902961305721, 8946835807050, 88648174014939, 878355088397901, 8703029361715560, 86232460051021149, 854419404714630381, 8465866782890863770
Offset: 1
Suppose the string is 00. At length 2 there are 99 strings that do not contain it. At length 3 there are 19 strings that do not contain it, 000, 00x, and x00, where x is any nonzero digit. So a(3) = 1000-19 = 981.
-
T[n_, k_] := LinearRecurrence[{n - 1, n - 1}, {n, n^2 - 1}, k];
T[10, {1, 19}] (* Robert P. P. McKone, Dec 31 2020 *)
A322053
Number of decimal strings of length n that contain a specific string xx (where x is a single digit).
Original entry on oeis.org
0, 1, 19, 280, 3691, 45739, 544870, 6315481, 71743159, 802527760, 8868438271, 97038694279, 1053164192950, 11351825985061, 121644911602099, 1296970638284440, 13767539948978851, 145580595285369619, 1534133217109136230, 16117424311550552641
Offset: 1
Suppose the desired string is 00. At length 2 that is the only possibility. At length 3 there are 19 strings that contain it: 000, 00d, and d00, where d is any nonzero digit.
A328916
Number of n-digit decimal numbers containing 123 as a substring.
Original entry on oeis.org
0, 0, 0, 1, 19, 280, 3699, 45971, 549430, 6390601, 72860039, 818050960, 9074118999, 99668329951, 1085865248550, 11749578366501, 126396115335059, 1352875288102040, 14417003302653899, 153043636911203931, 1619083493823937270, 17076417934936718801
Offset: 0
For n=6, there are a(6)=3699 six-digit numbers that contain 123 as a substring.
-
a = [0, 0, 0, 1]
for i in range(0, 18):
a.append(10 * a[len(a) - 1] + 9 * 10 ** (len(a) - 4) - a[len(a) - 3])
print(a)
Showing 1-4 of 4 results.
Comments